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Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity–wake interference region

Published online by Cambridge University Press:  12 February 2009

IMAN BORAZJANI  and
FOTIS SOTIROPOULOS
IMAN BORAZJANI
Affiliation:
St Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN, USA
FOTIS SOTIROPOULOS*
Affiliation:
St Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN, USA
*
†Email address for correspondence: fotis@umn.edu
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Abstract

We investigate numerically vortex-induced vibrations (VIV) of two identical two-dimensional elastically mounted cylinders in tandem in the proximity–wake interference regime at Reynolds number Re = 200 for systems having both one (transverse vibrations) and two (transverse and in-line) degrees of freedom (1-DOF and 2-DOF, respectively). For the 1-DOF system the computed results are in good qualitative agreement with available experiments at higher Reynolds numbers. Similar to these experiments our simulations reveal: (1) larger amplitudes of motion and a wider lock-in region for the tandem arrangement when compared with an isolated cylinder; (2) that at low reduced velocities the vibration amplitude of the front cylinder exceeds that of the rear cylinder; and (3) that above a threshold reduced velocity, large-amplitude VIV are excited for the rear cylinder with amplitudes significantly larger than those of the front cylinder. By analysing the simulated flow patterns we identify the VIV excitation mechanisms that lead to such complex responses and elucidate the near-wake vorticity dynamics and vortex-shedding modes excited in each case. We show that at low reduced velocities vortex shedding provides the initial excitation mechanism, which gives rise to a vertical separation between the two cylinders. When this vertical separation exceeds one cylinder diameter, however, a significant portion of the incoming flow is able to pass through the gap between the two cylinders and the gap-flow mechanism starts to dominate the VIV dynamics. The gap flow is able to periodically force either the top or the bottom shear layer of the front cylinder into the gap region, setting off a series of very complex vortex-to-vortex and vortex-to-cylinder interactions, which induces pressure gradients that result in a large oscillatory force in phase with the vortex shedding and lead to the experimentally observed larger vibration amplitudes. When the vortex shedding is the dominant mechanism the front cylinder vibration amplitude is larger than that of the rear cylinder. The reversing of this trend above a threshold reduced velocity is associated with the onset of the gap flow. The important role of the gap flow is further illustrated via a series of simulations for the 2-DOF system. We show that when the gap-flow mechanism is triggered, the 2-DOF system can develop and sustain large VIV amplitudes comparable to those observed in the corresponding (same reduced velocity) 1-DOF system. For sufficiently high reduced velocities, however, the two cylinders in the 2-DOF system approach each other, thus significantly reducing the size of the gap region. In such cases the gap flow is entirely eliminated, and the two cylinders vibrate together as a single body with vibration amplitudes up to 50% lower than the amplitudes of the corresponding 1-DOF in which the gap flow is active. Three-dimensional simulations are also carried out to examine the adequacy of two-dimensional simulations for describing the dynamic response of the tandem system at Re = 200. It is shown that even though the wake transitions to a weakly three-dimensional state when the gap flow is active, the three-dimensional modes are too weak to affect the dynamic response of the system, which is found to be identical to that obtained from the two-dimensional computations.

JFM classification

Aerodynamics: Flow-structure interactions Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 621 , 25 February 2009 , pp. 321 - 364
Copyright
Copyright © Cambridge University Press 2009

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Borazjani and Sotiropoulos supplementary material

Movie 1. This movie corresponds to figure 11 in the paper and visualizes the State 1 of the one degree of freedom case (as disscussed in the paper) by vorticity contours for two tandem cylinders at Ured=4 (Re = 200, Mred = 2, ξ = 0). The motion of the cylinders is restircted to the vertical direction.

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Borazjani and Sotiropoulos supplementary material

Movie 2. This movie corresponds to figure 12 in the paper and visualizes the State 2 of the one degree of freedom case (as disscussed in the paper) by vorticity contours for two tandem cylinders at Ured=8 (Re = 200, Mred = 2, ξ = 0). The motion of the cylinders is restircted to the vertical direction.

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Video 740.3 KB

Borazjani and Sotiropoulos supplementary material

Movie 3. This movie corresponds to figure 13 in the paper and visualizes the critical State of the one degree of freedom case (as disscussed in the paper) by vorticity contours for two tandem cylinders at Ured=5 (Re = 200, Mred = 2, ξ = 0). The motion of the cylinders is restircted to the vertical direction.

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Video 1.6 MB

Borazjani and Sotiropoulos supplementary material

Movie 4. This movie corresponds to figure 16 in the paper and visualizes the two degrees of freedom case (the cylinder is free to move both in horizental and vertical directions) by vorticity contours for two tandem cylinders at Ured=7 (Re = 200, Mred = 2, ξ = 0). In this case the cylinders come close to each other and shed as a single body.

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Video 324.6 KB

Borazjani and Sotiropoulos supplementary material

Movie 5. This movie corresponds to figure 20 in the paper and visualizes the three-dimensional two degrees of freedom case (the cylinder is free to move both in horizental and vertical directions) by the iso-surfaces of y-component of vorticity Ωy = ±0.1 (green and cyan) and z-component of vorticity Ωz = ±1.0 (Blue and red) for two tandem cylinders at Ured=6 (Re = 200, Mred = 2, ξ = 0).

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Video 3.8 MB